b) y" + 3y + 2y = e; y(0) = 0, y'(0) = 3 c) y" +9y= sin(2x); y(0) = 1, y'(0) = 0

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I only need help with parts b and c. Please show all steps clearly

4. Solve the following initial value problem:
a) y" + 4y = 2x; y(0) = 1, y'(0) = 2
b) y" + 3y' + 2y = e²; y(0) = 0, y'(0) = 3
c) y" +9y = sin(2x); y(0) = 1, y'(0) = 0
d) y(4) —y = 5; y(0) = y'(0) = y" (0) = y³) (0) = 0
Transcribed Image Text:4. Solve the following initial value problem: a) y" + 4y = 2x; y(0) = 1, y'(0) = 2 b) y" + 3y' + 2y = e²; y(0) = 0, y'(0) = 3 c) y" +9y = sin(2x); y(0) = 1, y'(0) = 0 d) y(4) —y = 5; y(0) = y'(0) = y" (0) = y³) (0) = 0
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